Transient spatiotemporal chaos is extensive in three reaction-diffusion networks

Stahlke, Dan; Wackerbauer, Renate

doi:10.1103/physreve.80.056211

Cited by 10 publications

(24 citation statements)

References 30 publications

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“…The transient nature of chaotic dynamics described above and shown in Figs. 5(c) and 5(d) is not new and has been found in several reaction-diffusion systems [51][52][53][54][55][56][57]. Since it is known that the chaos lifetime increases exponentially with system size [58], in the rest of this section we shall investigate the system size dependence of the chaotic dynamics by considering different system sizes.…”

Section: B Temporal and Spatiotemporal Chaosmentioning

confidence: 90%

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

2018

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In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (subT mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of subT-mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.

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Section: B Temporal and Spatiotemporal Chaosmentioning

confidence: 90%

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

2018

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“…Lattice (regular network) models are commonly used to describe nonlinear spatiotemporal dynamics (Cross and Hohenberg, 1993;Stahlke and Wackerbauer, 2009). We review several albedo parameterizations from the literature that are used in conceptual models.…”

Section: Model and Albedo Parameterizationmentioning

confidence: 99%

Albedo parametrization and reversibility of sea ice decay

Müller-Stoffels

Wackerbauer

2012

Nonlin. Processes Geophys.

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Abstract. The Arctic's sea ice cover has been receding rapidly in recent years, and global climate models typically predict a further decline over the next century. It is an open question whether a possible loss of Arctic sea ice is reversible. We study the stability of Arctic model sea ice in a conceptual, two-dimensional energy-based regular network model of the ice-ocean layer that considers ARM's longwave radiative budget data and SHEBA albedo measurements. Seasonal ice cover, perennial ice and perennial open water are asymptotic states accessible by the model. We show that the shape of albedo parameterization near the melting temperature differentiates between reversible continuous sea ice decrease under atmospheric forcing and hysteresis behavior. Fixed points induced solely by the surface energy budget are essential for understanding the interaction of surface energy with the radiative forcing and the underlying body of ice/water, particularly close to a bifurcation point. Future studies will explore ice edge stability and reversibility in this lattice model, generalized to a latitudinal transect with spatiotemporal lateral atmospheric heat transfer and high spatial resolution.

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“…∆ is a discrete N × N symmetric Laplacian matrix required to meet the condition N j=1 ∆ i j = 0. The network topology and boundary conditions are defined by ∆ [20].…”

Section: Reaction Diffusion Network Exhibiting Spatiotemporal Chaosmentioning

confidence: 99%

Length scale of interaction in spatiotemporal chaos

Stahlke

Wackerbauer

2011

Phys. Rev. E

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Extensive systems have no long scale correlations and behave as a sum of their parts. Various techniques are introduced to determine a characteristic length scale of interaction beyond which spatiotemporal chaos is extensive in reaction-diffusion networks. Information about network size, boundary condition, or abnormalities in network topology gets scrambled in spatiotemporal chaos, and the attenuation of information provides such characteristic length scales. Space-time information flow associated with the recovery of spatiotemporal chaos from finite perturbations, a concept somewhat opposite to the paradigm of Lyapunov exponents, defines another characteristic length scale. High-precision computational studies of asymptotic spatiotemporal chaos in the complex Ginzburg-Landau system and transient spatiotemporal chaos in the Gray-Scott network show that these different length scales are comparable and thus suitable to define a length scale of interaction. Preliminary studies demonstrate the relevance of these length scales for stable chaos.

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Transient spatiotemporal chaos is extensive in three reaction-diffusion networks

Cited by 10 publications

References 30 publications

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

Albedo parametrization and reversibility of sea ice decay

Length scale of interaction in spatiotemporal chaos

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